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PowerPoint Slideshow about 'Genetic Algorithms' - Patman

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For Example, let’s say that we are trying to optimize the following function,

f(x) = x2

for 2  x  1

If we were to use binary-coded representations we would first need to develop a mapping function form our genotype representation (binary string) to our phenotype representation (our CS). This can be done using the following mapping function:

In Proportionate Selection, individuals are assigned a probability of being selected based on their fitness:

pi = fi / fj

Where pi is the probability that individual i will be selected,

fi is the fitness of individual i, and

fj represents the sum of all the fitnesses of the individuals with the population.

This type of selection is similar to using a roulette wheel where the fitness of an individual is represented as proportionate slice of wheel. The wheel is then spun and the slice underneath the wheel when it stops determine which individual becomes a parent.

Crossover is usually the primary operator with mutation serving only as a mechanism to introduce diversity in the population.

However, when designing a GA to solve a problem it is not uncommon that one will have to develop unique crossover and mutation operators that take advantage of the structure of the CSs comprising the search space.

These GAs are characterized by the type of replacement strategies they use.

A Generational GA uses a (,) replacement strategy where the offspring replace the parents.

A Steady-State GA usually will select two parents, create 1-2 offspring which will replace the 1-2 worst individuals in the current population even if the offspring are worse than the individuals they replace.

Generation Gap: The fraction of the population that is replaced each cycle. A generation gap of 1.0 means that the whole population is replaced by the offspring. A generation gap of 0.01 (given a population size of 100) means ______________.

Elitism: The fraction of the population that is guaranteed to survive to the next cycle. An elitism rate of 0.99 (given a population size of 100) means ___________ and an elitism rate of 0.01 means _______________.

The Schema Theorem was developed by John Holland in an attempt to explain the quickness and efficiency of genetic search (for a Simple Genetic Algorithm).

His explanation was that GAs operate on large number of schemata, in parallel. These schemata can be seen as building-blocks. Thus, GAs solves problems by assembling building blocks similar to the way a child build structures with building blocks.

Although the above equation seems to say that above average schemata are allowed an exponentially increasing number of trials, instances may be gained or lost through the application of single-point crossover and mutation.